Regularization of subsolutions in discrete weak KAM theory

Patrick Bernard (1, 2) , Maxime Zavidovique (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 IMJ - Institut de Mathématiques de Jussieu

We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of $C^{1,1}$ subsolutions. Moreover, these subsolutions can be made strict and smooth outside of the Aubry set.

Domaines: Systèmes dynamiques [math.DS]

Patrick Bernard, Maxime Zavidovique. Regularization of subsolutions in discrete weak KAM theory. Canadian Journal of Mathematics, 2013, 65, pp.740-756. ⟨10.4153/CJM-2012-059-3⟩. ⟨hal-00678699v2⟩